Coterminal Angle Calculator

This coterminal angle calculator converts an angle in degrees or radians into two positive co-terminal angles, and two negative co-terminal angles.

Coterminal Angle Formula

Co-terminal angles are easy to calculator using the following formulas if in degrees.

Positive Coterminal Angle = Angle + 360

Negative Coterminal Angle = Angle -360

The formulas above would only yield one of each co terminal angles. In reality there are an infinite number of co terminal angles. The definition is simply an angle that ends at the same point as another angle on a the coordinate plane. Since the coordinate circle has as a total rotation of 360 degrees, adding or subtracting that to the angle yields a result as does the coterminal angle calculator above.

How to calculate a co terminal angle

Let’s take a look a tan example of how you might calculate the coterminal angle.

  1. Let’s assume you are given an angle in radians. For this example the angle is 2.5 radians.
  2. First, you must convert the radians to degrees. 1 radian is equal to 57.29 degrees so 2.5*57.28=114.59 degrees
  3. Last, we need to add 360 degrees to that angle to find an angle that is coterminal with the original angle, so 114.59+360 = 475.59 degrees.
  4. Check the answer using the calculator above.
coterminal angle calculator
What is a coterminal angle?

A coterminal angle is an angle that ends at the same location as another angle. For example, 1 degrees and 361 degrees are at the same location since the total angles in a circle is 360 degrees.

What is the coterminal angle formula?

The coterminal Angle can be calculated with one of the following:
Positive Coterminal Angle = Angle + 360
Negative Coterminal Angle = Angle -360

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